Certification Problem
Input (TPDB SRS_Standard/Waldmann_06_SRS/uni-6)
The rewrite relation of the following TRS is considered.
|
a(a(a(x1))) |
→ |
c(c(b(x1))) |
(1) |
|
b(b(b(x1))) |
→ |
c(c(c(x1))) |
(2) |
|
c(c(c(x1))) |
→ |
a(b(b(x1))) |
(3) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by AProVE @ termCOMP 2023)
1 Looping derivation
There is a looping derivation.
a a a b b b b →+ ε a a a b b b b ε
The derivation can be derived as follows.
-
a a a →+ c c b:
This is an original rule (OC1).
-
b b b →+ c c c:
This is an original rule (OC1).
-
c c c →+ a b b:
This is an original rule (OC1).
-
b b b →+ a b b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b b b →+ c c c
-
c c c →+ a b b
-
b b b b →+ a a b b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b b b →+ a b b
-
b b b →+ a b b
-
c c c b b →+ a a a b b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
c c c →+ a b b
-
b b b b →+ a a b b
-
c c c b b →+ c c b b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
c c c b b →+ a a a b b
-
a a a →+ c c b
-
b b b b b →+ c c b b b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
b b b →+ c c c
-
c c c b b →+ c c b b b
-
a a a b b b b →+ c c c c b b b:
The overlap closure is obtained from the following two overlap closures (OC2).
-
a a a →+ c c b
-
b b b b b →+ c c b b b
-
a a a b b b b →+ c a b b b b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a a b b b b →+ c c c c b b b
-
c c c →+ a b b
-
a a a b b b b →+ c a a b b b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a a b b b b →+ c a b b b b b
-
b b b →+ a b b
-
a a a b b b b →+ c a a a b b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a a b b b b →+ c a a b b b b
-
b b b →+ a b b
-
a a a b b b b →+ c c c b b b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a a b b b b →+ c a a a b b b
-
a a a →+ c c b
-
a a a b b b b →+ a b b b b b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a a b b b b →+ c c c b b b b
-
c c c →+ a b b
-
a a a b b b b →+ a a b b b b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a a b b b b →+ a b b b b b b
-
b b b →+ a b b
-
a a a b b b b →+ a a c c c b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a a b b b b →+ a a b b b b b
-
b b b →+ c c c
-
a a a b b b b →+ a a a b b b b:
The overlap closure is obtained from the following two overlap closures (OC3).
-
a a a b b b b →+ a a c c c b b
-
c c c →+ a b b